Wellcome

Inference for Heavy-Tailed Data : Applications in Insurance and Finance.

By: Peng, LiangMaterial type: TextTextPublisher: [Place of publication not identified] : Elsevier Science, 2017Description: 1 online resource (182 pages)Content type: text Media type: computer Carrier type: online resourceISBN: 012804750X; 9780128047507Subject(s): Mathematical statistics | Probabilities | MATHEMATICS -- Applied | MATHEMATICS -- Probability & Statistics -- General | Mathematical statistics | ProbabilitiesGenre/Form: Electronic books.Additional physical formats: Print version:: No titleDDC classification: 519.5/4 LOC classification: HG8076Online resources: ScienceDirect
Contents:
Front Cover; Inference for Heavy-Tailed Data; Copyright; Contents; About the Authors; Preface; 1 Introduction; 1.1 Basic Probability Theory; 1.2 Basic Extreme Value Theory; 2 Heavy Tailed Independent Data; 2.1 Heavy Tail; 2.2 Tail Index Estimation; 2.2.1 Hill Estimator; 2.2.1.1 Asymptotic Properties; 2.2.1.2 Optimal Choice of k; 2.2.1.3 Data Driven Methods for Choosing k; 2.2.1.4 Bias Corrected Estimation; 2.2.1.5 Sample Fraction Choice Motivated by Bias Corrected Estimation; 2.2.2 Other Tail Index Estimators; 2.3 High Quantile Estimation; 2.4 Extreme Tail Probability Estimation.
2.5 Interval Estimation2.5.1 Con dence Intervals for Tail Index; 2.5.1.1 Normal Approximation Method; 2.5.1.2 Bootstrap Method; 2.5.1.3 Empirical Likelihood Method; 2.5.2 Con dence Intervals for High Quantile; 2.6 Goodness-of-Fit Tests; 2.7 Estimation of Mean; 2.8 Expected Shortfall; 2.9 Haezendonck-Goovaerts (H-G) Risk Measure; 3 Heavy Tailed Dependent Data; 3.1 Tail Empirical Process and Tail Quantile Process; 3.2 Heavy Tailed Dependent Sequence; 3.3 ARMA Model; 3.4 Stochastic Difference Equations; 3.5 Heavy Tailed GARCH Sequences; 3.6 Double AR(1) Model; 3.7 Conditional Value-at-Risk.
3.8 Heavy Tailed AR-GARCH Sequences3.9 Self-Weighted Estimation for ARMA-GARCH Models; 3.10 Unit Root Tests With In nite Variance Errors; 4 Multivariate Regular Variation; 4.1 Multivariate Regular Variation; 4.2 Hidden Multivariate Regular Variation; 4.3 Tail Dependence and Extreme Risks Under Multivariate Regular Variation; 4.4 Loss Given Default Under Multivariate Regular Variation; 4.5 Estimating an Extreme Set Under Multivariate Regular Variation; 4.6 Extreme Geometric Quantiles Under Multivariate Regular Variation; 5 Applications; 5.1 Some Visualization Tools for Preliminary Analysis.
5.1.1 Hill Plot5.1.2 Alternative Hill Plot; 5.1.3 Log-Quantile Plot; 5.2 Heuristic Approach for Training Data; 5.3 Applications to Independent Data; 5.3.1 Automobile Bodily Injury Claims; 5.3.2 Automobile Insurance Claims; 5.3.3 Hospital Costs; 5.3.4 Danish Fire Losses Data; 5.4 Applications to Dependent Data; 5.4.1 Daily Foreign Exchange Rates; 5.4.2 Quarterly S & P 500 Indices; 5.4.3 S & P 500 Weighted Daily Returns; 5.5 Some Comments; A Tables; B List of Notations and Abbreviations; Bibliography; Index; Back Cover.
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Print version record.

Front Cover; Inference for Heavy-Tailed Data; Copyright; Contents; About the Authors; Preface; 1 Introduction; 1.1 Basic Probability Theory; 1.2 Basic Extreme Value Theory; 2 Heavy Tailed Independent Data; 2.1 Heavy Tail; 2.2 Tail Index Estimation; 2.2.1 Hill Estimator; 2.2.1.1 Asymptotic Properties; 2.2.1.2 Optimal Choice of k; 2.2.1.3 Data Driven Methods for Choosing k; 2.2.1.4 Bias Corrected Estimation; 2.2.1.5 Sample Fraction Choice Motivated by Bias Corrected Estimation; 2.2.2 Other Tail Index Estimators; 2.3 High Quantile Estimation; 2.4 Extreme Tail Probability Estimation.

2.5 Interval Estimation2.5.1 Con dence Intervals for Tail Index; 2.5.1.1 Normal Approximation Method; 2.5.1.2 Bootstrap Method; 2.5.1.3 Empirical Likelihood Method; 2.5.2 Con dence Intervals for High Quantile; 2.6 Goodness-of-Fit Tests; 2.7 Estimation of Mean; 2.8 Expected Shortfall; 2.9 Haezendonck-Goovaerts (H-G) Risk Measure; 3 Heavy Tailed Dependent Data; 3.1 Tail Empirical Process and Tail Quantile Process; 3.2 Heavy Tailed Dependent Sequence; 3.3 ARMA Model; 3.4 Stochastic Difference Equations; 3.5 Heavy Tailed GARCH Sequences; 3.6 Double AR(1) Model; 3.7 Conditional Value-at-Risk.

3.8 Heavy Tailed AR-GARCH Sequences3.9 Self-Weighted Estimation for ARMA-GARCH Models; 3.10 Unit Root Tests With In nite Variance Errors; 4 Multivariate Regular Variation; 4.1 Multivariate Regular Variation; 4.2 Hidden Multivariate Regular Variation; 4.3 Tail Dependence and Extreme Risks Under Multivariate Regular Variation; 4.4 Loss Given Default Under Multivariate Regular Variation; 4.5 Estimating an Extreme Set Under Multivariate Regular Variation; 4.6 Extreme Geometric Quantiles Under Multivariate Regular Variation; 5 Applications; 5.1 Some Visualization Tools for Preliminary Analysis.

5.1.1 Hill Plot5.1.2 Alternative Hill Plot; 5.1.3 Log-Quantile Plot; 5.2 Heuristic Approach for Training Data; 5.3 Applications to Independent Data; 5.3.1 Automobile Bodily Injury Claims; 5.3.2 Automobile Insurance Claims; 5.3.3 Hospital Costs; 5.3.4 Danish Fire Losses Data; 5.4 Applications to Dependent Data; 5.4.1 Daily Foreign Exchange Rates; 5.4.2 Quarterly S & P 500 Indices; 5.4.3 S & P 500 Weighted Daily Returns; 5.5 Some Comments; A Tables; B List of Notations and Abbreviations; Bibliography; Index; Back Cover.

Includes bibliographical references and index.

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